Following the recent controversy around Fox Searchlight’s “The Birth of a Nation,” fervor for the film about Nat Turner’s 1831 slave rebellion is down — including its Academy Award prospects. But with the film’s release in theaters nationwide this weekend, it might not be down for the entire count.

The picture pulled in an estimated $7.1 million in the U.S. and Canada, barely meeting analyst projections of $7 million to $9 million. The studio, which expected $7 million to $8 million going into the weekend, is happy with the debut, said Frank Rodriguez, Fox Searchlight’s senior vice president o...